Experimental evidence of the modulation of a plane wave to oblique perturbations and generation of rogue waves in finite water depth

Abstract

We present a laboratory experiment in a large directional wave basin to discuss the instability of a plane wave to oblique side band perturbations in finite water depth. Experimental observations, with the support of numerical simulations, confirm that a carrier wave becomes modulationally unstable even for relative water depths k0h < 1.36 (with k the wavenumber of the plane wave and h the water depth), when it is perturbed by appropriate oblique disturbances. Results corroborate that the underlying mechanism is still a plausible explanation for the generation of rogue waves in finite water depth

The North Sea Andrea storm and numerical simulations

“…Such results have been confirmed through recent numerical simulations of the Euler equations and experimental work performed in the MARINTEK Laboratories (Toffoli et al, 2011). The investigations have showed that the kurtosis, a measure of the probability of occurrence of extreme waves, depends on an angle β between the crossing wave systems.…”

“…The recognized mechanisms responsible for the occurrence of rogue waves can be classified as follows (Onorato et al, 2006a(Onorato et al, , b, 2010Toffoli et al, 2011;Didenkulova, 2010;Didenkulov and Pelinovsky, 2011;Sergeeva et al, 2011Sergeeva et al, , 2013: -shallow water effects.…”

“…As pointed out by Tomita (2009), both the numerical nonlinear wave models and the wave spectral models can be utilized in research of extreme and rogue waves and their use is encouraged. The complimentary nature of these models is clear; they give different information about a sea state.…”

Modulational instability and wave amplification in finite water depth

“…Under the influence of unstable side bands, however, modulational instability survives beyond this critical water depth and a significant amplification can be achieved also for relatively shallow water with k 0 h < 1.36, provided the perturbations are properly selected within the instability region. This is also in agreement with other experimental and numerical studies (Yuen and Lake, 1982;Trulsen and Dysthe, 1996;Trulsen et al, 1999;Tulin and Waseda, 1999;Gramstad and Trulsen, 2011;Toffoli et al, 2013). For relative water depth k 0 h = 0.8, simulations did not indicate any significant growing of the modulations, though.…”

“…It is important to mention that the timescales are consistent with the generation of rogue waves in the laboratory (see, in this regard, a recent comparison between experimental data and HOSM simulations in Toffoli et al, 2013).…”